What is (\partial)/(\partial x)(e^{-x/a}) ?

The answer to (\partial)/(\partial x)(e^{-x/a}) is -(e^{-x/a})/a

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(\partial)/(\partial x)(e^{-x/a})

\frac{\partial}{\partial x} (e^{- \frac{x}{a}})

- \frac{e ^{- \frac{x}{a}}}{a}

Solution steps

\frac{\partial}{\partial x} (e^{- \frac{x}{a}})

Apply the chain rule:

e^{- \frac{x}{a}} \frac{\partial}{\partial x} (- \frac{x}{a})

= e^{- \frac{x}{a}} \frac{\partial}{\partial x} (- \frac{x}{a})

\frac{\partial}{\partial x} (- \frac{x}{a}) = - \frac{1}{a}

= e^{- \frac{x}{a}} (- \frac{1}{a})

Simplify

e^{- \frac{x}{a}} (- \frac{1}{a}) : - \frac{e ^{- \frac{x}{a}}}{a}

= - \frac{e ^{- \frac{x}{a}}}{a}

\frac{\partial}{\partial y} (2 x + 3 y - 4)

\frac{\partial}{\partial y} (e^{x} y^{3} + 2 y e^{2 x})

\frac{d y}{d x} = - \frac{y}{10}

f (x) = x^{2} - 8, (2, - 4)

\int tan (x) 1 + sec^{4} (x) d x

What is (\partial)/(\partial x)(e^{-x/a}) ?
The answer to (\partial)/(\partial x)(e^{-x/a}) is -(e^{-x/a})/a